Occasional Paper No. 53

National Center for the Study of Privatization in Education

Teachers College, Columbia University

The Religious Factor in Private Education

July 2002

Danny Cohen-Zada and Moshe Justman

justman@bgumail.bgu.ac.il

Department of Economics Ben-Gurion University

Beer-Sheva, Israel

Abstract This paper quantifies the religious factor in education demand by calibrating a political economy model of education finance and school choice in which parents who differ in the advantage they attribute to religious education choose from among public, private-nonsectarian and religious schools. The calibrated distribution of religious preferences indicates that the revealed advantage of religious education is strongly contingent on its high levels of subsidization. The results of the calibration are applied to compare the effect of publicly funded vouchers that do not exclude religious schools—to which the Supreme Court recently opened a door in Zelman v. Simmons-Harris—with vouchers restricted to nonsectarian schools. It supports the implicit conclusion of the Court, that participation of religious schools in the Cleveland voucher program was essential for achieving its goal of helping low-income parents in a failing school district. Larger vouchers would have reduced the share of religious schools in the program, though they would still have attracted a majority of students. Keywords: religious education, public education, school finance, school vouchers JEL classification: H42, I22, I28

The Occasional Paper Series produced by the National Center for the Study of Privatization in Education promotes dialogue about the many facets of privatization in education. The subject matter of the papers is diverse, including research reviews and original research on vouchers, charter schools, home schooling, and educational management organizations. The papers are grounded in a range of disciplinary and methodological approaches. The views presented in this paper are those of the authors and do not necessarily represent the official views of the NCSPE.

If you are interested in submitting a paper, please contact: National Center for the Study of Privatization in Education Box 181, Teachers College, 525 W. 120th Street, New York NY 10027-6696 www.ncspe.org email: ncspe@columbia.edu

1. INTRODUCTION

The importance of the religious factor for private education in the United States is evident from

the large proportion of private school students—five out of six—attending religious schools.1

Commitment to religious values is clearly an important factor behind parents’ decisions to incur

the added expense of sending their children to private schools, but other factors are also at work:

religious education is often privately subsidized, and may also be perceived as more efficient

than public education.2 In Cleveland, a state-funded pilot voucher program gave low-income a

choice between religious and nonsectarian private schools, and almost all chose religious

schools: the vouchers were large enough to cover tuition in religious schools but not in private

nonsectarian schools, and the participating families could not afford to top them up. In a similar

but more generous program in Milwaukee, parents were offered vouchers that exceeded average

tuition in private nonsectarian elementary schools and about two thirds chose religious

schooling.3 The Supreme Court has recent ruled that the channeling of state funds to religious

schools through the Cleveland program voucher did not violate the Establishment Clause of the

First Amendment. This opens a door to further implementation of similarly structured programs

that include religious schools,4 which is likely to further expand religious education.

This paper quantifies the strength of the religious factor in education demand, and applies

its findings to compare vouchers that are restricted to nonsectarian schools with vouchers that

include religious education. Parents who choose religious schools for their children must view

these schools as providing a better education than local public schools, as the tuition they pay for

private education does not reduce their school-tax liabilities; and yet average tuition in private

religious schools is much lower than spending per pupil in public schools.5 This implies that

parents who choose religious schools must view a dollar of religious school tuition as buying

more education than a tax dollar spent on public education. Of course, this perceived advantage

is not shared by all parents, many of whom see religious instruction as a disadvantage. This

variety of religious sentiment implies a distribution of preferences for religious schooling, and it

is this distribution that we quantify here.

To this purpose we introduce a religious dimension in a political economy model of

education finance and school choice: households differ in their preferences for different types of

schools and choose between public, private-religious and private-nonsectarian schools based on

the added (or diminished) utility they derive from religious schooling, the degree to which

religious schools are subsidized, and the quality of public education.6 Public school spending is

determined by majority voting that anticipates households’ decisions on school choice. A

political-economy equilibrium in which these anticipations are correct is then derived.

Calibrating it to observed enrolment shares by school type, public spending on education, and the

parameters of the income distribution yields a distribution of the religious factor that underlies

observed patterns of school choice. It indicates that at current subsidy levels, three out of four

households prefer religious to nonsectarian education, but that few households would prefer

religious education if religious and nonsectarian schools were equally subsidized.

The results of the calibration are then applied to compare, through simulations, vouchers

restricted to nonsectarian schools to vouchers that include religious schools.7 These indicate that

vouchers must be large enough to cover, or nearly cover, private tuition to have a significant

effect on the low-income households that such programs are generally intended to help. Hence

vouchers restricted to nonsectarian schools must be considerably larger than the Cleveland

vouchers to have a significant effect on private enrolment, and even then our calibration

indicates that a majority of households would choose religious education no matter how large the

amount of the voucher. Only if religious schools are included in the program can smaller sized

vouchers reach low-income families. This supports the implicit conclusion of the Supreme Court,

that participation of religious schools in the Cleveland voucher program was essential for

achieving its goal of assisting low-income parents in a failing school district, and suggests that

similar findings are likely to apply in other settings. Comparing voucher effects across states, we

find substantial variety in the magnitude of local responses similarly structured voucher

programs, suggesting that moderately sized vouchers will only be effective in location where

substantial existing religious enrolment indicates strong religious sentiment. Finally, we find that

if vouchers are restricted to low-income families (that would not otherwise enroll in private

schools), and the marginal savings to the public system from the exit of a voucher recipient is

greater than the sum of the voucher, then the voucher program should generate modest fiscal

benefits in the long run, though transition costs may be substantial.8

The structure of the paper is as follows: Section 2 defines the model, derives its basic

properties and characterizes its political-economic equilibrium; Section 3 calibrates it to national

and state-level data; Section 4 applies the calibrated model to school voucher programs; Section

5 discusses various extensions; and Section 6 concludes.

2. FORMAL ANALYSIS

2.1 Basic definition of the model

Consider an economy with a continuum of households of measure one, indexed by i, each

comprising one parent and one child. Each household is characterized by its income yi and by a

religious parameter zi > 0 that reflects the intrinsic value it attaches to a religious education.9 Let

g(y, z) denote the joint density function of y and z, let ym denote median household income, and

let Y denote mean income. Household utility then depends on: consumption of a numeraire good

c; the quality of education, measured as spending per pupil in the child’s school, x;10 and the

religious orientation of the household’s school of choice given the nature of its own religious

sentiment, z. To fix ideas, set household utility equal to:

U (ci , xi , zi) =

ci α xi

1− α if household i chooses a secular school

ci α (zi xi)

1− α if household i chooses a religious school (1)

where 0 < α < 1 is a fixed, common parameter. Thus households with zi < 1 view religious

schooling as a drawback per se, though they may opt for a religious school if it is sufficiently

subsidized (and their value of zi is not too small), while households with zi > 1 view religious

schooling as an advantage.

Public education is available free of charge to all households at a uniform quality x

funded by a proportional income tax rate t levied on all households and determined by majority

vote.11 Denoting by q the proportion of households that send their children to public schools, and

choosing quality units so that the price of public school quality equals one, the government’s

balanced budget constraint implies that the quality of public schooling is

x = t Y / q (2)

Nonsectarian private schooling and religious private schooling are available as alternatives to

public schooling, and can be purchased from a competitively priced private sector in any desired

quality, though doing so does not reduce one’s tax liability. We assume that the cost of a unit of

education quality in nonsectarian schools is the same as in public schools, while stipulating that

religious school tuition is subsidized at the rate h.12

2.2 School choice

The indirect utility anticipated by a household with income yi sending its child to public school

equals:

Vp ( yi, t, qe) = [(1 – t) yi ]

α [ t Y / qe ] 1 − α (3)

where qe is the level of public enrolment that it anticipates. A household with income yi that

sends its children to a nonsectarian private school solves:

max c,x cα x 1− α subject to c + x = (1 – t) yi (4)

obtaining indirect utility

Vn (yi, t) = α α (1 − α)1−α (1 – t) yi (5)

And a household with income yi and religious preference zi that sends its child to a religious

private school solves:

max c,x cα (zi x) 1−α subject to c + (1 – h) x = (1 – t) yi (6)

and obtains indirect utility

Vr ( yi, zi, t) = [zi / (1 – h)]1–α αα (1 − α)1−α (1 – t) yi (7)

As the model does not separate between the effect of the religious preference parameter zi and

the effect of the subsidy for religious schooling h, we simplify the notation by setting ki =

zi / (1 – h), and denote by f (y, k) its induced joint density function with y.13 It follows from direct

comparison of (5) and (7) that households prefer private religious schooling to private secular

schooling if and only if ki > 1, and to simplify the exposition we assume that when parents are

indifferent between secular and religious schooling they choose secular schooling.

As opting out of public education does not reduce one’s tax obligations, sending one’s

child to private school must be aimed at obtaining a higher quality of education; and as education

quality is a normal good, households that favor a given type of private school over public

schooling will be those with higher incomes. A household with ki < 1 chooses between public

and private-nonsectarian schooling by comparing the utility levels in equations (3) and (5).

Given a tax level t and anticipated public enrolment qe, either all households with ki < 1 prefer

public education, or there exists a threshold income yn (t, qe) implicitly defined by

Vp (yn, t, qe ) = Vn (yn, t) (8)

such that households with ki < 1 and income above yn (and only those households) send their

children to nonsectarian private schools (figure 1).14 Private nonsectarian enrolment is then

( )∫ ∫∞

=1

0 ),(

,),(e

n qty

en dkdykyfqtq (9)

Similarly, a household with ki > 1 chooses between public and religious schooling by comparing

(3) and (7), and for a given tax level t and anticipated public enrolment share qe sends its child to

a religious school if and only if its income exceeds the threshold yr (ki, t, qe) implicitly defined

by15

Vp (yr, t, qe) = Vr ( yr, ki (1 – h) , t) (10)

(See figures 1 and 2). Private religious enrolment then equals

( )∫ ∫∞ ∞

=1 ),,(

,),(e

r qtky

er dkdykyfqtq (11)

In equilibrium we require that, given the tax rate t, the actual public enrollment rate equals the

anticipated rate, i.e., we seek a value of q = q (t) that solves:

( ) ( )∫ ∫∫ ∫∞

+=−−=1

),,(

0

1

0

),(

0

,,),(),(1)(qtkyqty

rn

rn

dkdykyfdkdykyfqtqqtqtq (12)

Differentiation of (8) and (10) with respect to q reveals that both yn and yr are decreasing in q,

and as the value of the right-hand side of (12) at q = 1 is non-negative, and its value at q = 0 is

no greater that 1, for each t there exists a unique equilibrium value of public enrolment q(t),

implicitly defined by (12), that equates anticipated and actual enrolment rates.

2.3 Voting on the tax rate

Under our assumption of a Cobb-Douglas utility function, all households that anticipate sending

their children to public school prefer the same tax rate, which is characterized by the first-order

condition

dVp /dt = (1 – t)α –1 (y / x )α [ –α x + (1 – α) (1 − t ) d x / d t ] = 0 (13)

where x (t) = t Y / q (t) , and q (t) is defined by the solution to (12). Assuming a majority of

households choose public education,16 equation (13) determines the tax rate.

3. CALIBRATION

3.1 Calibration to national averages

We calibrate the model initially to average United States data.17 Assume that both the

distribution of income in the population and the distribution of the parameter k follow lognormal

distributions: ln y ~ N (µy, σy2) and ln k ∼ N (µk, σk

2), and that the two variables are uncorrelated.

The joint distribution of ln y and ln k is then bivariate normal with zero correlation, and the joint

density of y and k is given by

−+

−⋅−

=

22 lnln5.0

21

),(y

y

k

kyk

yk

ekyfσ

µ

σµ

σπσ (14)

The parameters of the income distribution are calibrated directly from the actual distribution of

household income in the United States in 1998. Under the assumption of a lognormal distribution

of income, median income is ym = exp(µy) and mean income is Y = exp(µy + σy2/2). Setting Y

equal to mean household income in that year, $52,513, and ym equal to median household

income,18 $38,885, gives µy = 10.57 and σy 2 = 0.601.

The parameters µk and σk2 that determine the distribution of k, along with α the parameter

of the utility function, are calibrated from the tax rate, which we set equal to the share of public

spending on education in household income, and which must satisfy equation (12); and from

enrolment shares in private-secular and private-religious education. To set the tax rate, note that

public expenditure per pupil equals tY / qm where m is the ratio of pupils to households. Setting

tY / qm = $6,189, m = 0.507, and q = 0.901—their actual values in 1997/8—and taking average

household income Y as above, yields a tax rate of t = 5.38%.19

Incorporating the lognormal specification in equations (9) and (11) we obtain the

following expressions for the share of households that opted for private-secular and private-

religious education, which are set equal to actual enrolment shares in 1997/1998:20

( )∫ ∫∞

=1

0 ),(

,qty

n

n

dkdykyfq = 0.0156 (9a)

( )∫ ∫∞ ∞

=1 ),,(

,qtky

r

r

dkdykyfq = 0.0836 (11a)

Substituting equation (8) in (9a) and (10) in (11a), and requiring that equation (12) is satisfied,

gives three equations in the three unknowns α, µk and σk . The calibrated values of the household

preference parameters that we obtain from solving these equations are: α = 0.933,

µk = 0.148, and σk = 0.232, implying that the mean value of k is 1.190, its median value is 1.158,

and its standard deviation is 0.279. It follows that 74% of households have k values over 1, and

hence prefer religious education to private nonsectarian education, if funding is independent of

school choice. This is roughly consistent with parents’ choices in the Milwaukee voucher

program: given vouchers that exceeded average tuition at both religious and nonsectarian private

elementary schools, two thirds chose religious schools.

3.2 Measuring the relative efficiency of religious schools

The distribution of the parameter k is not in itself a measure of the relative efficiency of religious

schools as it also includes a subsidy term, h, the rate at which tuition in religious schools is

privately subsidized. The inherently subjective, multi-dimensional quality of religious education

is represented in our model by the distribution of the parameter z. Recalling that ln ki = ln zi – ln

(1 – h), identifying the distribution of z is equivalent to measuring h. But this is far from

straightforward: parish subsidies may be partially offset by tacit requirements that parents donate

their own time or money to the school; and lower salaries in religious schools may or may not

reflect differences in teacher quality (see note 2). Furthermore, the school choices that underpin

our calibrated value of k are a reflection of the subjective quality of locally available religious

schools, and in this regard reflect not only individual preferences but also conditions of supply.

The implications of different values of h for the distribution of z are presented in Table 1, the last

column of which is the share of the population with z > 1, i.e., the share of the population that

views the religious schools to which it has access as more desirable, without a subsidy, than local

public schools. This share varies widely: 74% if h = 0, 37% if h = 20%, 18% if h = 30%, 6% if h

= 40%, and 1% if h = 50%. This implies that if religious schools are as heavily subsidized as the

raw data suggest—as much as 50% in Catholic schools (see note 2)—then only a very small

minority of the population finds these schools subjectively more cost-effective than public

schools.

3.3 Sensitivity analysis

To check the sensitivity of our calibration to specific parameter values, we varied each parameter

individually around its national value. The results of are presented in Table 2. Both the mean and

median values of k vary in narrow ranges, about ±5% around their calibrated values, while its

standard deviation varies more, ranging between 0.194 and 0.546.

3.4 Calibration to state data

Calibrating the model to state data serves both to check the sensitivity of the calibration to

national data and as a basis for analyzing the impact of local conditions on voucher outcomes, in

the following section. Basic descriptive data for all states are presented in Table 3, and the

calibration results are reported in Table 4. Calibration was successful for 37 states. The mean

value of k has an average value of 1.196 over these states, very near its calibrated value from

national data, 1.190; it ranges from a minimum of 0.988 to a maximum of 1.467; and has a

standard deviation of 0.134. It is closely correlated with the share of religious schools in total

enrolment in the state. A regression of mean k values on religious enrolment shares qr across

states yielded the equation: k = 0.86 + 4.08*qr with an R2 value of 0.916. The median value of k

behaves similarly, with a mean value of 1.126, very near the value calibrated from national data,

1.158, a range of 0.807 to 1.328, and a standard deviation of 0.131. The standard deviation of k

varies more widely, between 0.052 and 1.396, with a mean value of 0.384 and a standard

deviation of 0.272.

There were thirteen states for which we were not able to calibrate the model, presumably

because their parameters were not consistent with our theoretical framework. Six states

(Arkansas, Nevada, North Dakota, Texas, West Virginia, Wyoming) are characterized by

surprisingly low private enrolment rates given their high income inequality, which may be

attributable to low population densities that, together with initially increasing returns to scale,

raise the relative cost of private education—a factor that does not enter in our model. A second

group of six states (Alabama, Delaware, Maine, Maryland, Mississippi, Vermont) is

characterized higher private enrolment rates than might be expected given their levels of income

inequality. This too may be a supply-side phenomenon: private schools locating in these states

for unique historical or geographical reasons not represented in the model, and attracting large

numbers of out-of-state pupils.21 The thirteenth state, Utah, is characterized by an exceptionally

low religious enrolment rate, possible attributable to the unique religious composition of its

population.

4. SCHOOL VOUCHERS

In this section we apply the results of the calibration to gauge the effects of differently structured

school voucher programs on enrolment shares and public spending per pupil. We assume

throughout that the tax rate is fixed at 5.38% of household income; the amount of the voucher is

exogenously determined, and not so large as to draw a majority of households out of public

education; and the voucher program is financed from the same tax base as public education, so

that its cost is deducted from the public school budget.22 The voucher program is allowed to vary

in three dimensions: the size of the voucher; whether its use is restricted to nonsectarian schools

or “unrestricted” and available for use in both nonsectarian and religious schools; and whether or

not it is means-tested, i.e., available only to households below some given income. We begin

with the simplest case, that of an unrestricted voucher available to all households, which we then

compare to vouchers available only for use in nonsectarian schools and to means-tested

vouchers.

4.1 Unrestricted vouchers offered to all households for use in all schools

Consider a voucher of exogenous magnitude s funded from the same tax base as expenditure on

public schools and offered to all households for use in any private school they choose. Assume

all households have the same number of children, m, and that each treats its children identically.

Spending per pupil in public schools is then

x (t, q, s) = [t Y – (1 – q) s m ] / (q m) (15)

and the indirect utility of a household that chooses public education equals

Vps (yi) = [(1 – t) yi ]α x 1−α (16)

Households that send their children to nonsectarian private schools have indirect utility:23

Vns (yi, ki) =[ ] [ ]

[ ] [ ]

−−≥+−−

−−<−

−−

−

)1)(1(//)1()1(

)1)(1(/)1(

11

1

tmsymsmyt

tmsyyts

ii

ii

αααα

αα

ααα

αα

(17)

And households that send their children to religious private schools have indirect utility:24

Vrs (yi, ki) =[ ] [ ]

[ ] [ ]

−−≥+−−

−−<−

−−−

−

)1)(1(//)1()1(

)1)(1(/)1()(

111

1

tmsymsmytk

tmsyytsk

iii

iii

αααα

αα

αααα

αα

(18)

Setting (16) equal to (17) determines a threshold income level yns (t, qe, s) defined by

Vps (yns) = Vns (yns) (19)

such that all households with ki < 1 and income below yns send their children to public schools

while those with ki < 1 and income above yns send their children to private nonsectarian

schools,25 and the private nonsectarian enrolment share equals

( )∫ ∫∞

=1

0 ),,(

,)(sqty

en

ens

dydkkyfqq (20)

Next, comparing (16) and (18) for a given value of ki > 1, we distinguish between two cases. If ki

< x / s then there exists a threshold income yrs (ki, t, qe, s) defined implicitly by

Vps(yrs) = Vrs(yrs , ki) (21)

such that households with k = ki and income yi above yrs choose religious schooling (see figure

3a); and if ki > x / s then all households with k = ki choose religious schooling (figure 3b), and

we set yrs (ki, t, qe, s) = 0. The enrolment share of religious schools then equals

( )∫ ∫∞ ∞

=1 ),,,(

,)(sqtky

er

ers

dkdykyfqq (22)

In equilibrium we require that realized public enrollment equal its anticipated value, and seek q

that solves:

q = 1 – qn (q) – qr (q) (23)

for the given voucher amount s, the given tax rate t = 5.38%, and the parameter values calibrated

in the preceding section.

Table 5 presents the effect on enrolment and spending of unrestricted vouchers in

increments of $1,000, from $1,000 to $5,000. The impact on private enrolment is substantial,

especially in religious schools, and each has a positive though small impact on public spending

per pupil, indicating a Pareto improvement over the no-voucher case.26 The fall in public

enrolment below 50% when a voucher of $5,000 is offered points to the possibility of large

unrestricted vouchers ultimately undermining the viability of public education. It suggests that

on purely fiscal grounds, and ignoring the social benefits of public education, a majority of

households may prefer to replace the public education system with a pure voucher program. We

consider this issue further in section 5.

4.2 Vouchers restricted to non-sectarian schools (without a means test)

Now consider the effect of explicitly incorporating in the model an exogenous restriction that

prevents the use of tax dollars to finance vouchers for religious schools, and assume for the

moment that such vouchers are available to all households regardless of income. Spending per

pupil in public schools is then given by

x = (t y – qn s m) / (q m) (24)

and indirect utility from public education is

Vp1 (y) = [(1 – t) y]α x 1−α (25)

Indirect utility when private nonsectarian schooling is chosen equals

Vn1 (yi) =[ ] [ ]

[ ] [ ]

−−≥+−−

−−<−

−−

−

)1)(1(//)1()1(

)1)(1(/)1(

11

1

tmsymsmyt

tmsyyts

ii

ii

αααα

αα

ααα

αα

(26)

and indirect utility when religious schooling is chosen equals

Vr1 (y, k) = αα (1 − α)1−α k 1–α(1 – t) y / m1–α (27)

As above, all households with ki < 1 prefer private non-sectarian schooling to religious

schooling, and hence send their children to nonsectarian private schools if and only if their

income exceeds a threshold level yn1(t, qe, qne, s) defined by Vp1 (yn1) = Vn1 (yn1). However,

households with k > 1 may now prefer private nonsectarian schooling to private religious

schooling because only the former allows them to take advantage of the voucher program. Thus a

household with k > 1 sends its children to private religious school if it meets two conditions: It

must prefer religious to public schooling, which holds if its income exceeds the threshold level

yrp1(k, t, qe, qne , s

) defined by (the positive root of) Vp1 (yrp1) = Vr1 (yrp1,k); and it must prefer

religious to private nonsectarian schooling, which holds if its income exceeds the threshold level

yrn (k, t, s ) defined by Vn1 (yrn1) = Vr1 (yrn, k).27 Denote yr1(ki ; t, qe, qn

e, s) = max { yrp1, yrn};

then private religious enrolment equals

( )∫ ∫∞ ∞

=1 ),,,,(1

,),(sqqtky

en

er

en

er

dkdykyfqqq (28)

A household with income yi and ki > 1 chooses private-nonsectarian education if it prefers it to

both public and religious education (figure 4a), which holds if

yn1(t, qe , qn

e , s ) < yi < yrn(ki , t, s

) (29)

Inspection of (27) reveals that yrn is decreasing in k so that for sufficiently high values of k, we

may have yn1 > yrn1 in which case households with such values of k never choose private-secular

schooling (figure 4b). Let k1 (t, qe, qn

e , s ) be the smallest value of k for which yn1 > yrn. The

share of private nonsectarian enrolment is then:

( ) ( )∫ ∫∫ ∫ +=∞ ),,,(

1

),,(

),,,(

1

0 ),,,,(

1

11

,,),(sqqtk stky

sqqtysqqtky

en

en

en

ern

en

en

en

en

dkdykyfdkdykyfqqq (30)

The model is then solved by requiring that anticipated enrolment shares in public and private-

secular education accord with household decisions, i.e., we seek q* and qn* such that q* = 1 – qr

(q*, qn*) – qn (q*, qn*) and qn* = qn (q*, qn*) , where qr (q

e, qne) and qn (q

e, qne) are defined by

equations (28) and (30).

The results of these calculations for vouchers restricted to non-sectarian schools, in

increments of $1,000 between $1,000 and $5,000, holding the tax rate fixed at t = 5.38%, are

presented in Table 6. The relative effect on private non-sectarian enrolment is substantial—a

$2,000 voucher more than doubles the private non-sectarian share—but because of its small

absolute size, and because some of the increase is drawn from private religious enrolment, the

impact on public enrolment is small. Moreover, the beneficiaries of these programs are

exclusively higher income households, many of which would have opted for private education

without the voucher. Consequently spending per pupil in public education falls slightly, and the

program has a detrimental effect on low-income households.

4.3 Means-tested vouchers

Means-tested vouchers available for use in both nonsectarian and religious schools offered to

low-income families in Cleveland under Ohio’s Pilot Project Scholarship Program, and in a

similar program in Milwaukee, induced extensive enrolment of children from underprivileged

homes in private religious schools. As we show here, this result is not surprising and is likely to

be replicated in other localities where similarly structured programs are put into place.

Furthermore, vouchers targeted exclusively at low-income families should also induce slight

increases in public spending per pupil, holding the tax rate fixed, if the exit of students from the

public system generates proportional savings (Chen and West, 2000; Bearse et al., 2000).

Let y denote the maximal income for participating in the voucher program. Then, as

vouchers are unrestricted with regard to type of school, households with ki > 1 that choose

private schooling choose religious schooling, while households with ki < 1 that choose private

schooling choose nonsectarian schooling. Spending per pupil in public education is then a

function of public enrolment q and of the share of households that meet the means test and

choose private education, π:

x ( q, π ) = [ t Y – π s m ] / (q m) (31)

Comparing indirect utility levels across school types within each of the four types of households

(ki < 1, y > y;), (ki < 1, y < y;), (ki >1, y > y) and (ki >1, y < y;) yields four threshold income

levels: ynh (t, s, qe, πe), ynl (t, s, qe, πe), yrh (t, s, qe, πe) and yrl (k, t, s, qe, πe) such that each

household chooses private education (of the type it prefers) if and only if its income exceeds the

relevant threshold.28 Private nonsectarian enrollment is then:

( ) ( )∫ ∫∫ ∫∞

+=1

0 ),,,(

1

0 ),,,(

,,),(ee

nhee

nl qsty

y

qsty

een dkdykyfdkdykyfqq

ππ

π (32)

private religious enrollment is

( ) ( )∫ ∫∫ ∫∞ ∞∞

+=1 ),,,,(1 ),,,,(

,,),(ee

rhee

rl qstky

y

qstky

eer dkdykyfdkdykyfqq

ππ

π (33)

and the share of households that use a voucher is

( ) ( )∫ ∫∫ ∫∞

+=1 ),,,,(

1

0 ),,,(

,,),(y

qstky

y

qsty

ee

eerl

eenl

dkdykyfdkdykyfqππ

ππ (34)

The model is then solved by requiring that anticipated public enrolment and voucher use accord

with household decisions. Thus we seek q* and π* such that q* = 1 – qr (q*, π *) – qn (q*, π *)

and π * = π (q*, π *) where the functions qr (qe, π e), qn (q

e, π e) and π (qe, π e) are defined by

equations (32) – (34).

The results are presented in Table 7 for vouchers of $3,000 and $4,000, and means tests

between $20,000 and $80,000. Religious enrolment increases substantially, with the size of the

increase depending strongly on the size of the voucher and the stringency of the means test. For

the larger voucher, religious enrolment increases by more than half when the means test is set at

$40,000 and more than doubles when it is set at $80,000. Public spending per pupil increases

throughout, increasing more the larger the voucher and the higher the threshold (within the given

range), though the largest increase is no more than 4%. This increase incidentally causes a slight

decline in nonsectarian private enrolment. Clearly, in terms of the model, an unrestricted means-

tested voucher of $4,000 is a Pareto improvement over no voucher: households that choose to

remain in the public school system benefit from higher spending per pupil without an increase in

taxes; households that take advantage of the voucher clearly gain; and those above the means test

are no worse off than before.29

4.4 Restricting means-tested vouchers to nonsectarian schools

Restricting vouchers to nonsectarian schools virtually precludes their use by lower-income

households unless they are offered in very generous amounts. Low-income families will only use

a voucher if it is sufficient in itself to obtain a better education than local public schools can

offer.30 If voucher amounts are not very large, only subsidized religious schools will accept it in

full payment of tuition; nonsectarian schools that do not have access to similar charitable sources

will require additional tuition. In the context of our model, our calculations show that even a

$5,000 voucher restricted to non-sectarian schools would not be taken up by households earning

less than $40,000 annually.31 While this result should not be taken literally—costs are lower for

elementary schools than for high schools, private nonsectarian schools may be more efficient

than public schools in failing school districts, and may offer reduced tuition to disadvantaged

children for a variety of reasons (a sense of public service, the value of a diverse student body,

marginal costs that are below average costs)—its essence is clear. It supports the conclusion

implicit in the Court’s ruling on Zelman v. Simmons-Harris, that the primary objective of Ohio’s

pilot voucher program—to provide greater educational opportunity for underprivileged students

in a failing public school system—could not have be achieved if the program had excluded

religious schools, unless of course it offered much larger vouchers than those it provided.32

4.5 Voucher simulations using the results of calibrations to state data

To test the sensitivity of these results to variation in the parameters of the model across states we

computed the impact of an unrestricted means-tested voucher equal to one half of public

spending per student in the state and available to households with no more than median state

income, for the 37 states for which we were able to calibrate the model. The results are presented

in table 8, and show large variation between the states. Thus while the national calibration

indicates a decline of one half a percentage point in public enrolment and a similar rise in

religious enrolment, seven states show declines in public enrolment (and increases in religious

enrolment) of more than 5 percentage points, while in nine others the change is less than 0.05

percentage points. In general, the magnitude of the change varies closely with the mean and

standard deviation of the religious factor k, which itself is strongly correlated with religious

enrolment in the state.33 Holding the tax rate fixed and assuming that each student opting out of

public education generates cost savings equal to average spending per student in the state before

implementation of the voucher program, an increase in public spending per student is inevitable,

as the sum of the voucher is half this amount and the means test is sufficiently stringent to

exclude virtually all families that sent their children to private schools before the program is

implemented. However, the relative increase is small—approximately half the size of the

reduction in public enrolment and never more than 4%. These increases, which represent

improvements in public education in the context of the model, lead to slight declines in

nonsectarian private enrolment of up to 0.2 percentage points.

5. DISCUSSION

In this section we discuss in more general terms various extensions of the model that bear on the

preceding analysis.

5.1 Endogenous determination of the sum of the voucher

In the preceding sections we assumed that the tax rate and voucher amounts were exogenously

determined, and focused on their effect on enrolment. Now allow endogenous determination of

the amount of the voucher by majority vote while holding the tax rate fixed, retaining the

assumption that there are no external funding sources, and restricting our attention to vouchers

that leave a majority of households attending public schools.34 Then voters who anticipate

sending their children to public schools—the majority—all prefer the voucher amount that

maximizes public spending per pupil. Letting t0 denote the fixed tax, this is the voucher that

satisfies ∂ ),( 0 stx /∂ s = 0 , where sstx ∂∂ /),( 0 is obtained by total differentiation of the relevant

equilibrium conditions.35 Applying this observation to the voucher programs considered in the

preceding section, it follows that of the different configurations presented in Tables 5, 6 and 7, a

voucher of $4,000 available to households with incomes below $80,000 for use in any type of

private school would command a majority over all other voucher programs described in these

tables.36

5.2 Endogenous determination of the tax rate

Assume now that the tax rate is determined endogenously by popular vote before the voucher

amount is similarly chosen. Let s*(t) denote the voucher amount chosen contingent on the tax

rate t, again restricting our attention to vouchers that leave the majority of households in public

schools. Our choice of utility function then implies that all these households prefer the same tax

rate, which—after applying the envelope theorem—satisfies

t / ( 1 − t ) = [(1−α) / α] [∂ ))(*,( tstx /∂ t ] / [ ))(*,( tstx / t] (35)

Numerical simulations indicate that the partial elasticity [∂ ),( stx /∂ t ] / [ ))(*,( tstx / t] is small

for our calibration, implying little variation in the tax rate—as long as there is a majority in favor

of public schooling.37

5.3 The viability of public education

The narrow focus of Ohio’s Pilot Project Scholarship Program on helping low-income families

in a failing school district, and the modest sums of money involved, were key elements in the

Supreme Court’s landmark ruling on Zelman v. Simmons-Harris,38 which suggests that a

program broad enough to allow a majority of families in a school district to opt out of public

education, might not have earned the Court’s approval. However, if unrestricted voucher funding

of religious education should be allowed, our analysis suggests that, holding the tax rate fixed, a

majority coalition of religious and high-income households would prefer receiving an

unrestricted voucher and having public education discontinued, to a public education system

without vouchers.

To see that this is consistent with our calibration, let q0 denote the fraction of households

attending public education before vouchers are introduced. Households with values of k > 1/q0

prefer that public education be discontinued and all tax revenues used to fund an unrestricted

voucher of sum tY, which they could apply towards tuition in religious schools and obtain a

preferred education for their children.39 They would be joined by households with income in

excess of some threshold ys that would supplement the voucher amount to obtain a higher quality

education than currently offered by public schools.40 Noting that 1/q = 1.1 is less than the median

value of k calibrated from national data, 1.15, and less than the median value of k for 25 of the 37

states for which we calibrated the model, such a majority is likely to exist provided religious

schools are able to maintain current subsidy levels while substantially expanding their enrolment.

This suggests that continued public support for public education rests on other considerations:

regard for the constitutional separation of religion and government; subscription to the principle

of equal opportunity embodied in public education; an appreciation of the external benefits of a

public education system in reducing crime and ethnic strife, and promoting communal values;

and so on.

Mixed systems that combine unrestricted means-tested vouchers with public education

may be preferred by a majority of households to either a pure public system and a pure voucher

system. Our calibration indicates that an unrestricted means-tested voucher of $4,000 offered to

households with income under $80,000 as an alternative to public education would be preferred

by a majority of households to either pure system.

5.4 The supply of private education and the direct costs of privatization

Empirical evidence suggests that tuition at parochial schools may be subsidized by as much as

50%, through private donations, institutional support from the church and reduced salaries paid

to teachers in religious orders, thought this may be partially offset if parents are expected to

supplement tuition with contributions of money or time that raise the cost of schooling.

However, current subsidy levels for tuition in parochial schools may be difficult to maintain if

parish support or the supply of teachers in religious orders cannot keep pace with increases in

enrolment.

We assume in our analysis that the cost of “education quality” in private nonsectarian

schools is the same as in public schools, but this is certainly not always the case. Moreover,

variation in the cost of quality may also be observed within public education: in poorly managed

school districts the imputed cost of quality is much higher than in well-managed districts. While

a theoretical extension along these lines is easily done, relating the parameters of the model to

observed variables is less straightforward. Non-academic dimensions of quality cloud its

measurement; and self-selection introduces further variety in student motivation and parental

support that may be difficult to identify.

Supply side factors can also affect schooling costs when voucher programs change

enrolment patterns. In small school districts, scale effects can substantially lower average costs

when enrolment expands and raise them when it contracts. The availability of voucher support is

likely to increase the variety of religious options, especially in smaller school districts, which

should further increase the attraction of private religious education. In addition, as the calibration

to state data indicated, there are other factors, such as population density, as well as historical

and geographical factors, that affect the local supply of private education but do not enter our

analysis.

Moreover, the process of school choice itself requires additional resources, from schools

and parents (Levin and Driver, 1997). Experience with open enrolment suggests that as schools

become dependent on voucher income they need to devote substantial resources to marketing

efforts; and parents facing wider choices need to collect more information, monitor school

performance more closely, and generally deal with a school administration that has at least one

eye on the bottom line.41 Finally, cost savings from reducing public enrolment materialize more

slowly than the added cost of funding the vouchers, generating a negative fiscal impact in the

short term, even if the long-term effect is positive.

5.5 Other extensions of the model

The joint distribution of income, religious preferences and family size. The model can

accommodate almost without change alternative assumptions regarding the correlation between

religion and income, replacing our assumption of a zero correlation. It is also readily extended to

allow for a variable number of children in the family, again with possibly nonzero correlations

between family size, income and religious inclination. And the model could also be extended to

allow conditions of extreme poverty or affluence to exercise a “non-linear” effect on school

choice, by using a more general utility function.

Institutional factors. Our simple analysis ignores important institutional detail, such as state and

federal sources of external funding, the precise nature of the tax base, and the electoral process

through which education budgets are approved, which vary substantially from one school district

to another. We skirt these issues by assuming that the design of the voucher program is

exogenously determined (the small net fiscal effects generated by the programs we consider here

imply that the source of voucher funding has little impact on individual school choice, on which

we focus in this paper). Extending the analysis to incorporate the fiscal relations between local

and state jurisdictions would allow us explicitly to consider the political economy of how

voucher programs are shaped.42

Other important factors. Other important dimensions of religious education not addressed in this

paper could be addressed in extensions of the model that combined a distribution of religious

preferences with other aspects of the political economy of education. Hoxby (2002) argues that

school choice improves the efficiency of public schools through competitive pressure,

specifically documenting the beneficial effect of the Milwaukee voucher program on

productivity in local public schools.43 Others warn that the wide use of vouchers for private

schools may erode popular support for ailing public schools. Peer-group effects generated by the

movement of pupils from public to private schools may promote inequality by increasing

stratification, thus benefiting the strong but hobbling the weak; such effects have been

incorporated in school choice models by Epple and Romano (1998), among others. Schools that

promote different value systems, through vouchers or other means, may undermine the

important role of public education in strengthening the fabric of society and increase racial,

ethnic or religious divisions.44 Finally, the localized structure of school finance in the United

States implies that school funding and school choice are closely linked to property values,

migration and competition between local jurisdictions. These issues have been integrated and

quantitatively analyzed by Epple and Sieg (1999) and Nechyba (2000).

6. CONCLUDING REMARKS

The recent ruling of the Supreme Court on the constitutionality of Ohio’s pilot voucher program

reflects a growing recognition that alternative modes of education finance may be needed to

improve the quality of education for underprivileged children. Limited prior experience with

pilot programs suggests that if voucher sums are moderate, nonsectarian private schools do not

offer a viable option for low-income families. The Court’s ruling that indirect voucher support

for religious schools need not violate the constitutional separation of religion and government

opens a door to voucher programs that include religious schools.

This paper offers a methodological framework for anticipating the impact of such

programs, in lieu of direct empirical evidence, which as yet is limited. It uses current data on

enrolment shares and tax rates to calibrate a political economy model of education finance and

school choice that incorporates a religious dimension, which reveals the distribution of

preferences for religious education. This is then used to gauge the effects of differently designed

voucher programs on enrolment shares. The results confirm the hypothesis that moderately sized

vouchers restricted to nonsectarian schools can have little affect on low-income families, and

demonstrate the stronger impact of voucher programs that include religious schools, while

indicating that the advantage of religious schools is contingent on their high levels of

subsidization. Comparing calibrations of the model across states highlights large differences

among them, indicating that states with low religious enrolment will need to offer more generous

vouchers to achieve significant results.

In focusing our analysis on the religious dimension of private education we have ignored

other important dimensions of voucher reform with which it should be integrated: interaction

between state and local funding of public schools; peer-group effects that result from the

changing composition of school populations; the benefits of competition between schools; a

closer analysis of cost factors; reciprocal effects between schools, local property values and

residential mobility; and the potential impact of a large increase in religious schooling on social

discord. Integrating the religious dimension of education with these different elements offers

extensive scope for further research.

REFERENCES

Bearse, P., Glomm, G. and Ravikumar, B., 2000. On the political economy of means-tested education vouchers. European Economic Review 44, 904-15.

Buddin, R., Cordes, J. and Kirby, S. N., 1998. School choice in California: Who chooses private schools? Journal of Urban Economics 44, 110-134.

Card, D. and Krueger, A. 1996. Labor market effects of school quality: Theory and evidence. NBER WP 5708.

Chen, Z. and E. G. West, 2000. Selective versus universal vouchers: Modeling median voter preferences in education. American Economic Review 90, 1520-1534.

Clotfelter, C., 1976. School desegregation, “tipping” and private school enrolment. Journal of Human Resources 11, 28-50.

Epple, D. and Sieg, H. 1999. Estimating equilibrium models of local jurisdictions. Journal of Political Economy 107, 645-682.

Epple, D. and Romano, R. E., 1998. Competition between private and public schools, vouchers and peer-group effects. American Economic Review 88, 33-62.

Epple, D. and Romano, R. E., 1996. Ends against the middle: Determining public service provision when there are private alternatives. Journal of Public Economics 62, 297-325.

Evans, W. and Robert, S., 1995. Finishing high school and starting college: Do Catholic schools make a difference? Quarterly Journal of Economics 110, 947-74.

Fernandez, R. and Rogerson, R., 1999. Education finance reform and investment in human capital: Lessons from California. Journal of Public Economics, 74(3), 327-350.

Fiske, E. B. and Ladd, H. F., 2000. When Schools Compete. Washington, DC: Brookings.

Friedman, M., 1962, The role of government in education. In Capitalism and Freedom, Chapter VI. Chicago: University of Chicago Press.

Friedman, M., 2002. The market can transform our schools. New York Times July 2.

Glazer, Nathan, 2001. Seasons Change. Education Next (Fall) pp. 34-37.

Glomm, G. and Ravikumar, B., 1998. Opting out of publicly provided services: A majority voting result. Social Choice and Welfare 15, 187-199.

Hanushek, E., 1996. School resources and student performance. In G. Bartles, ed., Does money matter? The effect of school revenues on student achievement and adult success, pp. 43-73.

Howell, W. G. and Peterson, P. E., 2002. The Education Gap. Washington, DC: Brookings.

Hoxby, C. M., 2002. School choice and school productivity (or Could school choice be a tide that lifts all boats?) NBER WP 8873

Hoxby, C. M., 1998. What do America’s ‘traditional’ forms of school choice teach us about school choice reforms? Federal Reserve Bank of New York Economic Policy Review 4, 47-59.

Hoyt, W. and Lee, K., 1998. Educational vouchers, welfare effects and voting. Journal of Public Economics 69, 211-228.

James, E., 1987. The public-private division of responsibility for education: An international comparison. Economics of Education Review 6,1-14.

Krueger, A., 1998. Reassessing the view that American schools are broken. Federal Reserve Bank of New York Economic Policy Review 4, 29-43.

Levin, H. M. and Driver, C. E., 1997. Costs of an Educational Voucher System. Educational Economics 5(3) 265-283.

Martinello, F., and West, E. G., 1988, The optimal size of the tuition tax credit, Public Finance Quarterly, 16, 425-438.

National Center for Education Statistics, 2000. Digest of Educational Statistics 2000.

National Catholic Educational Association, 2001. Balance Sheet for Catholic Elementary Schools: 2001.

National Catholic Educational Association, 1990. United States Catholic Elementary and Secondary Schools 1989-90.

Nechyba, T. J., 2000. Mobility, targeting and private school vouchers. American Economic Review 90, 130-146.

New York Times, 2002. Voucher backers see opening for a wider agenda. June 28.

New York Times, 2001a. Schools are now marketers where choice is taking hold. April 20

New York Times, 2001b. As bid to privatize schools ends, supporters second-guess effort. March 31.

Paine, Thomas, 1792. Rights of Man, Part 2. Reissued by Wordsworth Editions, 1996.

Rangazas, P., 1995. Vouchers and voting: An initial estimate based on the median voter model. Public Choice 82, 261-79.

Romer, T., Rosenthal, H. and V. Munley, 1992. Economic incentives and political institutions: Spending and voting in school-budget referenda. Journal of Public Economics 49, 1-33.

Sander, W., 1997. Catholic high schools and rural academic achievement. American Journal of Agricultural Economics 79, 1-12.

Sonstelie, J., 1982. The welfare cost of free public schools. Journal of Political Economy 90, 794-808.

Smith, Adam, 1776. An Inquiry into the Nature and Causes of the Wealth of Nations. Reissued by Everyman’s Library, 1991.

U.S. Census Bureau, Statistical Abstract of the United States 2000.

West, E., 1997. Education vouchers in principle and practice: A survey. World Bank Research Observer 12, 83-103.

Zelman et al. v. Simmons-Harris et al., U.S. Supreme Court No. 00-1751, decided June 27, 2002, http://laws.findlaw.com/us/000/00-1751.html.

Table 1. Distribution of the religious preference parameter z for different values of the subsidy factor h

h E (ln z) SD (ln z) E (z) SD (z) Prob ( z > 1)

0 0.15 0.23 1.19 0.28 74%

10% 0.04 0.23 1.07 0.25 57%

20% -0.08 0.23 0.95 0.22 37%

30% -0.21 0.23 0.83 0.20 18%

40% -0.36 0.23 0.71 0.17 6%

50% -0.55 0.23 0.60 0.14 1%

Table 2. Sensitivity of the calibration to variation in individual parameter values

Parameter (base value) Parameter value Mean k Std dev k Median k

4.38% 1.187 0.271 1.157 Share of public spending in income (5.38%) 6.38% 1.194 0.287 1.161

0.64 1.165 0.208 1.147 Median to mean income ratio (0.74) 0.84 1.152 0.546 1.041

7.4% 1.148 0.206 1.130 Private religious enrolment share (8.4%) 9.4% 1.235 0.341 1.191

1.0% 1.184 0.194 1.169 Private nonsectarian enrolment share (1.55%) 2.0% 1.187 0.362 1.135

Table 3. State data

State Mean income (household)

Median to mean ratio

Public education share in income

Religious enrolment

Private secular enrolment

Alabama 41,815 0.867 5.22% 6.05% 2.77% Alaska 54,373 0.932 9.35% 4.29% 0.23% Arizona 45,673 0.812 4.65% 4.19% 1.04% Arkansas 39,678 0.697 5.58% 4.78% 0.74% California 58,454 0.700 4.90% 7.54% 1.97% Colorado 54,357 0.857 4.58% 5.41% 1.70% Connecticut 73,608 0.632 5.23% 8.36% 3.10% Delaware 57,687 0.719 5.07% 14.66% 3.11% Florida 48,840 0.715 4.43% 8.78% 1.88% Georgia 50,127 0.771 5.45% 4.94% 2.28% Hawaii 57,143 0.714 4.85% 13.17% 1.75% Idaho 43,199 0.849 5.96% 3.45% 0.35% Illinois 58,286 0.741 4.82% 12.07% 0.93% Indiana 47,415 0.838 5.89% 9.09% 0.55% Iowa 45,564 0.812 5.98% 8.93% 0.17% Kansas 48,526 0.757 5.54% 7.35% 0.62% Kentucky 41,940 0.864 5.56% 8.63% 0.93% Louisiana 43,254 0.734 5.83% 13.26% 2.17% Maine 43,361 0.822 6.75% 3.84% 3.64% Maryland 59,990 0.834 5.11% 10.99% 2.53% Massachusetts 62,960 0.673 4.99% 8.51% 3.31% Michigan 51,213 0.817 6.35% 9.25% 0.68% Minnesota 54,068 0.886 5.63% 8.89% 0.69% Mississippi 38,704 0.752 5.61% 5.56% 4.19% Missouri 47,078 0.854 5.15% 10.50% 1.10% Montana 37,955 0.832 7.08% 4.56% 0.33% Nebraska 47,897 0.760 5.72% 12.05% 0.23% Nevada 52,630 0.755 4.41% 3.43% 0.72% New Hampshire 56,597 0.794 4.87% 6.53% 2.96% New Jersey 69,543 0.716 5.86% 12.18% 1.92% New Mexico 41,004 0.769 6.41% 4.04% 1.44% New York 63,095 0.593 5.93% 12.15% 1.89% North Carolina 46,507 0.771 4.85% 4.82% 1.83% North Dakota 40,948 0.740 5.93% 5.65% 0.18% Ohio 48,823 0.797 5.47% 11.11% 0.88% Oklahoma 40,451 0.834 6.02% 3.88% 0.37% Oregon 47,165 0.828 5.73% 6.35% 1.21% Pennsylvania 51,840 0.753 5.50% 14.37% 1.53% Rhode Island 51,646 0.788 6.26% 11.80% 2.51% South Carolina 41,880 0.794 5.81% 5.45% 2.40% South Dakota 42,957 0.763 5.59% 6.09% 0.34% Tennessee 45,226 0.754 4.64% 7.03% 1.63% Texas 51,521 0.695 5.78% 4.65% 0.77% Utah 48,996 0.904 5.78% 1.62% 0.93% Vermont 45,303 0.869 7.17% 4.04% 5.23% Virginia 53,196 0.815 4.91% 5.95% 2.18% Washington 53,676 0.883 5.04% 6.05% 1.16% West Virginia 36,579 0.730 7.28% 4.23% 0.40% Wisconsin 49,290 0.838 6.46% 13.11% 0.89% Wyoming 44,826 0.786 7.28% 2.14% 0.46%

Table 4. Calibration to state data (selected states; see text)

State Religious enrolment Mean k

Standard dev k Median k á Mean ln k

(ìk) Std dev ln k (ók

2) Alaska 4.29% 1.095 0.521 0.988 0.890 -0.012 0.452 Arizona 4.19% 1.062 0.090 1.058 0.945 0.056 0.085 California 7.54% 1.144 0.251 1.118 0.940 0.111 0.216 Colorado 5.41% 1.035 0.476 0.941 0.944 -0.061 0.438 Connecticut 8.36% 1.173 0.524 1.071 0.936 0.069 0.427 Florida 8.78% 1.201 0.332 1.157 0.945 0.146 0.271 Georgia 4.94% 1.056 0.230 1.032 0.935 0.032 0.215 Hawaii 13.17% 1.418 0.641 1.293 0.937 0.257 0.431 Idaho 3.45% 1.070 0.061 1.069 0.932 0.067 0.057 Illinois 12.07% 1.347 0.352 1.303 0.937 0.265 0.257 Indiana 9.09% 1.262 0.247 1.239 0.923 0.214 0.194 Iowa 8.93% 1.239 0.143 1.231 0.924 0.208 0.115 Kansas 7.35% 1.140 0.118 1.134 0.933 0.126 0.103 Kentucky 8.63% 1.240 0.378 1.186 0.927 0.171 0.298 Louisiana 13.26% 1.424 0.875 1.213 0.924 0.193 0.566 Massachusetts 8.51% 1.159 0.655 1.010 0.939 0.010 0.526 Michigan 9.25% 1.258 0.255 1.232 0.918 0.209 0.201 Minnesota 8.89% 1.264 0.383 1.210 0.925 0.190 0.296 Missouri 10.50% 1.287 0.472 1.208 0.931 0.189 0.355 Montana 4.56% 1.098 0.077 1.095 0.917 0.091 0.070 Nebraska 12.05% 1.337 0.212 1.320 0.925 0.278 0.157 New Hampshire 6.53% 0.988 0.700 0.807 0.940 -0.215 0.637 New Jersey 12.18% 1.370 0.624 1.247 0.924 0.220 0.435 New Mexico 4.04% 1.029 0.052 1.028 0.926 0.027 0.050 New York 12.15% 1.413 0.596 1.302 0.926 0.264 0.405 North Carolina 4.82% 1.061 0.143 1.051 0.942 0.050 0.134 Ohio 11.11% 1.314 0.337 1.273 0.928 0.242 0.253 Oklahoma 3.88% 1.065 0.054 1.064 0.930 0.062 0.051 Oregon 6.35% 1.152 0.262 1.123 0.929 0.116 0.225 Pennsylvania 14.37% 1.467 0.689 1.328 0.926 0.284 0.446 Rhode Island 11.80% 1.300 1.396 0.886 0.920 -0.121 0.876 South Carolina 5.45% 1.051 0.371 0.991 0.929 -0.009 0.343 South Dakota 6.09% 1.076 0.052 1.075 0.934 0.072 0.048 Tennessee 7.03% 1.137 0.224 1.116 0.943 0.110 0.195 Virginia 5.95% 1.069 0.419 0.996 0.939 -0.005 0.378 Washington 6.05% 1.074 0.534 0.961 0.938 -0.040 0.470 Wisconsin 13.11% 1.388 0.477 1.313 0.910 0.272 0.334 US 8.36% 1.190 0.279 1.159 0.933 0.148 0.232

Table 5. Universal unrestricted vouchers

Voucher amount Public

spending per pupil

Public enrolment

Nonsectarian private

enrolment

Religious enrolment

no voucher $6,189 90.1% 1.56% 8.36%

$1,000 $6,195 88.1% 1.84% 10.09% $2,000 $6,195 85.2% 2.20% 12.57% $3,000 $6,197 80.6% 2.70% 16.74%

$4,000 $6,249 70.0% 3.37% 26.60%

$5,000 $6,221 47.1% 4.63% 48.26%

Table 6. Universal vouchers restricted to non-sectarian schools

Voucher amount Public

spending per pupil

Public enrolment

Nonsectarian private

enrolment

Religious enrolment

no voucher $6,189 90.1% 1.56 % 8.36 %

$1,000 $6,186 89.74% 2.34% 7.91%

$2,000 $6,176 89.10% 3.59% 7.30%

$3,000 $6,152 87.88% 5.63% 6.49%

$4,000 $6,099 85.41% 9.14% 5.45%

$5,000 $5,986 79.49% 16.33% 4.18%

Table 7. Means-tested, unrestricted vouchers

Maximum qualifying income

Public spending per

pupil

Public enrolment

Nonsectarian private

enrolment

Religious enrolment

$3,000 voucher

$20,000 $6,192 90.0% 1.56 % 8.47 %

$40,000 $6,203 89.6% 1.55 % 8.80 %

$60,000 $6,241 88.5% 1.53% 10.00%

$80,000 $6,306 86.3% 1.48 % 12.20 %

$4,000 voucher

$20,000 $6,228 88.3% 1.53 % 10.22 %

$40,000 $6,290 85.5% 1.50 % 13.02 %

$60,000 $6,360 82.5% 1.45 % 16.00 %

$80,000 $6,435 79.3% 1.41 % 19.27 %

Table 8. Effect of a voucher equal to 50% of state public spending per student, available to households with up to median state income, for use in all schools, by state

Percentage point change in:

Pre-voucher religious enrolment

share

Mean k (from

table 4)

Proportionate change in

public spending per pupil

Public enrolment

Nonsectarian private

enrolment

Enrolment in religious schools

Alaska 4.3% 1.095 1.8% -3.8 0.0 3.8 Arizona 4.2% 1.062 0.0% 0.0 0.0 0.0 California 7.5% 1.144 0.1% -0.2 0.0 0.2 Colorado 5.4% 1.035 1.1% -2.4 -0.1 2.5 Connecticut 8.4% 1.173 1.6% -3.1 -0.1 3.2 Florida 8.8% 1.201 0.6% -1.1 0.0 1.1 Georgia 4.9% 1.056 0.0% -0.1 0.0 0.1 Hawaii 13.2% 1.418 3.5% -6.4 -0.2 6.5 Idaho 3.5% 1.070 0.0% 0.0 0.0 0.0 Illinois 12.1% 1.347 1.3% -2.4 0.0 2.4 Indiana 9.1% 1.262 0.4% -0.8 0.0 0.8 Iowa 8.9% 1.239 -0.1% 0.0 0.0 0.0 Kansas 7.4% 1.140 0.0% 0.0 0.0 0.0 Kentucky 8.6% 1.240 1.4% -2.8 -0.1 2.9 Louisiana 13.3% 1.424 4.0% -7.6 -0.2 7.8 Massachusetts 8.5% 1.159 2.2% -4.2 -0.2 4.3 Michigan 9.3% 1.258 0.4% -0.8 0.0 0.8 Minnesota 8.9% 1.264 1.7% -3.5 0.0 3.5 Missouri 10.5% 1.287 2.2% -4.4 -0.1 4.5 Montana 4.6% 1.098 0.0% 0.0 0.0 0.0 Nebraska 12.1% 1.337 0.2% -0.4 0.0 0.4 New Hampshire 6.5% 0.988 1.7% -3.5 -0.1 3.6 New Jersey 12.2% 1.370 3.1% -5.7 -0.1 5.9 New Mexico 4.0% 1.029 0.0% 0.0 0.0 0.0 New York 12.2% 1.413 3.2% -5.8 -0.1 5.9 North Carolina 4.8% 1.061 0.0% 0.0 0.0 0.0 Ohio 11.1% 1.314 1.1% -2.2 0.0 2.2 Oklahoma 3.9% 1.065 0.0% 0.0 0.0 0.0 Oregon 6.4% 1.152 0.2% -0.5 0.0 0.5 Pennsylvania 14.4% 1.467 3.9% -7.3 -0.2 7.5 Rhode Island 11.8% 1.300 3.1% -6.8 -0.2 7.1 South Carolina 5.5% 1.051 0.6% -1.2 0.0 1.2 South Dakota 6.1% 1.076 0.0% 0.0 0.0 0.0 Tennessee 7.0% 1.137 0.1% -0.1 0.0 0.1 Virginia 6.0% 1.069 0.9% -1.8 -0.1 1.9 Washington 6.1% 1.074 1.6% -3.4 -0.1 3.5 Wisconsin 13.1% 1.388 2.7% -5.4 -0.1 5.5 US 8.4% 1.190 0.3% -0.5 0.0 0.6

yn

y

Figure . The distribution of households among school types (schematic representation)

1

public

religious

private nonsectarian

k

yr(k)

Vp(y)

Vn(y)

Vr(k,y)

y

V

yn yr(k)

Figure 2. School choice in a household with k > 1

Figure 3. School choice with unrestricted vouchers

Vps(y)

Vns(y) Vrs(k,y)

y

V

yns yrs(k)

Vps(y)

Vns(y)

Vrs(k,y)

y

V

yns yrs(k) = 0

(b)

(a)

αsm (1–α)(1–t)

αsm (1–α)(1–t)

Vp1(y)

Vn1(y) Vr1(k,y)

y

V

yn1 yrn(k)

yrp1(k) = yr1(k)

(b)

Vp1(y)

Vn1(y)

Vr1(k,y)

y

V

yn1 yrn(k) = yr1(k) yrp1(k)

Figure 4: School choice with vouchers restricted to nonsectarian schools

(a)

αsm (1–α)(1–t)

αsm (1–α)(1–t)

Appendix A. Threshold levels for unrestricted means-tested vouchers

The threshold levels are determined by setting the indirect utility values offered by the different

school types equal to each other. In the first three cases we solve:

[(1 – t) �nh ]α [ (t Y –πe s m ) / (qe m)] 1−α = αα (1 − α)1−α (1 – t) �nh / m1−α

[(1 – t) �nl ]α [ (t Y – πe s m) / (qe m)] 1−α = αα (1 − α)1−α [(1 – t) �nl + s m] / m1−α

[(1 – t) �rh ]α [ (t Y – π e s m ) / (qe m)] 1−α = ki

1–α αα (1 − α)1−α (1 – t) �rh / m1−α

and set ynh = max {�nh , y}; ynl = min {�nl , y} ; and yrh = max {�rh , y}. In the fourth case we

take into account the possibility that a low-income household with k > 1 may take advantage of

the voucher without adding to it. This happens if and only if ki > sx / , in which case all

households with this k and income below the means test use a voucher, and we set �rl = 0. If 1 <

ki < sx / then �rl is the larger root that solves

[(1 – t) �rl]α [(tY – πesm) / (qem) ]1−α = ki

1–α αα(1−α)1−α [(1 – t) �rl + sm]

and we set yrl = min {�rl , y}.

Appendix B. Means-tested vouchers restricted to nonsectarian schools

In this case, spending per pupil in public education is a function of public enrolment q and of the

share of households meeting the means test that choose private nonsectarian education π:

x ( q, π) = ( t Y – π s m ) / (q m)

Utility from public education is then

Vp2 = [(1 – t) yi ]α [ (t Y – πe s m ) / (qe m)] 1−α

As households that opt for religious schooling are now not eligible for the voucher, utility from

religious education is

Vr2 = αα (1 − α)1−α k1-α (1 – t) y / m1−α

All households with ki < 1 prefer private nonsectarian schooling to religious schooling, and

again, for these households we have two thresholds between public and private nonsectarian

schooling: one for lower-income households who meet the means test, y < y, and are eligible for

the voucher; and another for higher income households who choose private education though not

eligible for a voucher. The threshold income level between public and private nonsectarian

schooling for households who are eligible for the voucher, �nl, is implicitly defined by

[(1 – t) �nl ]α [ (t Y – πe s m) / (qe m)] 1−α = αα (1 − α)1−α [(1 – t) �nl + s m] / m1−α

and, as before, let ynl = min {�nl , y}. The threshold income, �nh, between public and private

nonsectarian schooling for households not eligible for the voucher, is implicitly defined by

[(1 – t) �nh ]α [ (t Y – πe s m ) / (qe m)] 1−α = αα (1 − α)1−α (1 – t) �nh / m1−α

and denote ynh = max {�nh , y}.

The difference between this case and the case of unrestricted means-tested vouchers is that in

this case households with k > 1 and y < y may prefer private secular to private religious schooling

because only the former allows them to take advantage of the voucher program. A household

with income y < y and k > 1 sends its children to a private nonsectarian school if it prefers it to

both public and private religious schooling. It prefers private nonsectarian schooling to public

schooling if its income exceeds the threshold level ynl (t, qe, πe, s) defined above; and it prefers

private nonsectarian schooling to religious schooling if its income is lower than the threshold

level yrn (k, t, s ) defined by

αα (1 − α)1−α [(1 – t) yrn + s m] / m1−α = αα (1 − α)1−α k1-α (1 – t) yrn / m1−α .

Private nonsectarian enrollment is then

( ) ( ) ( )∫ ∫∫ ∫∫ ∫∞∞

++=1

0

1

01

},min{

,,,),(nhnl

rn

nl y

y

y

yy

y

een dydkkyfdydkkyfdydkkyfqq π (C1)

A household prefers religious schooling to public schooling if its income exceeds the threshold

yrp2 defined implicitly by

αα (1 − α)1−α k1–α (1 – t) yrp2 / m1−α =[(1 – t) yrp2 ]α [ (t Y – πe s m ) / (qe m)] 1−α

Private religious enrollment is then

( )[ ]

( )[ ]

∫ ∫∫ ∫∞ ∞∞

+=1 ,max1 ,max 22

,,),(yy

y

yy

eer

rprnrp

dydkkyfdydkkyfqq π (C2)

and the share of households that use a voucher is

( ) ( )∫ ∫∫ ∫∞

+=1

},min{1

0

,,),(yy

y

y

y

eern

nlnl

dydkkyfdydkkyfq ππ (C3)

The model is then solved by requiring that anticipated public enrolment and voucher use accord

with household decisions, i.e., we seek q* and π1* such that q* = 1 – qr (q*, π*) – qn (q*, π *)

and π* = π (q*, π*) where the functions qr (qe, πe), qn (q

e, πe) and π (qe, π e) are defined by

equations (C1) – (C3).

1 In 1997/8, there were 5,076,119 students enrolled in private schools in the United States, about 10% of total K-12 enrolment. Of these, 2,514,699 attended Catholic schools and 1,764,447 other religious private schools, together accounting for 84.2% of total private enrolment (Digest of Educational Statistics, 2000, Table 60). Econometric estimates of the demand for private schooling consistently attribute a prominent role to religious factors, in the United States as in other countries (Clotfelter, 1976; James, 1987; Buddin et al., 1998; among many others). 2 The link between religious affiliation and school choice is evident in the large proportion of Catholic school pupils who come from Catholic homes (87.9% in 1989/90; National Catholic Educational Association, 1990). The effect of subsidies on this proportion is evident from the Cleveland voucher program, where a large fraction of participating families have been Baptists who send their children to Catholic schools, as only one Baptist school participated in the program (Zelman v. Simmons-Harris, footnote 11). Hoxby (1998) estimated that charitable subsidies from all sources reduce tuition costs in religious schools by as much as 50%; Catholic elementary schools received 24.1% of their revenues from parish subsidies in 2000/2001, and average salaries received by religious sisters serving as principals in these schools were 60% lower than those of public school principals (National Catholic Education Association, 2001, cited in Zelman v. Simmons-Harris footnote 15). However, tuition may not fully reflect private costs if parents are expected to supplement it with donations of their own time or money, as is often the case in religious schools. Of course, differences in tuition are not an accurate measure of cost differences unless they control for quality. Studies that measure the relative academic achievement of Catholic schools (Evans and Robert, 1995; Sander, 1997) partly address this issue, but ignore other, necessarily subjective dimensions of quality that are especially important with regard to religious schools. Hence the need to gauge quality and cost-effectiveness from revealed preferences. 3 Both programs are aimed at low-income families in failing school districts. In Cleveland, vouchers of up to $2,250 were offered, and 96% of voucher recipients opted for religious schools (Zelman v. Simmons-Harris). In Milwaukee, where vouchers of more than $5,000 were offered, two thirds chose religious schools (Hoxby, 2002). In 1993/4, average tuition was $1,628 in Catholic elementary schools, $2,606 in other religious schools, and $4,693 in private nonsectarian schools; the corresponding figures for secondary schools were $3,643, $5,261 and $9,525 (Digest of Education Statistics, 2000, Table 62) 4 The Supreme Court’s ruling in Zelman v. Simmons-Harris reversed lower-court decisions that enjoined the State of Ohio from offering vouchers for religious private schools to low-income parents in the Cleveland City School District, determining that the program was not in violation of the Establishment Clause of the First Amendment to the Constitution prohibiting the federal government from enacting laws that advance or inhibit religion, extended by the Fourteenth Amendment to state governments. The court reached this decision “(b)ecause the program was enacted for the valid secular purpose of providing educational assistance to poor children in a demonstrably failing public school system … “ and “…is neutral with respect to religion and provides assistance directly to a broad class of citizens who, in turn, direct government aid to religious schools wholly as a result of their own genuine and independent private choice.”

5 In 1993/4 spending per pupil in public elementary and secondary schools was $5,767, compared to average tuition of $2,178 in Catholic schools and $2,915 in other religious schools (Digest of Education Statistics, 2000, Tables 170, 62) 6 This extends work by Sonstelie (1982), Martinello and West (1988), Rangazas (1995), Epple and Romano (1996), Bearse et al. (2000), Nechyba (2000) among others. Sonstelie (1982) applied his analysis to estimate the difference in efficiency between private and public schooling, albeit as a single value rather than a distribution, and—absent a distinction between religious and nonsectarian schools—without recognizing that the choice of school may be influenced by religious sentiment and private subsidization, as well as cost-efficiency. 7 The use of calibrated theoretical models supplements direct evidence on the effect of school vouchers, from pilot and experimental programs in the United States (e.g., Howell and Peterson, 2002), and international experience, especially in Chile and New Zealand (West, 1997; Fiske and Ladd, 2000) 8 The costs of the program are immediate; the savings generated by students leaving the public system materialize gradually. Levin and Driver (1997) estimate that “accommodating additional students, record keeping, student transportation, information to parents and dispute adjudication … could raise public education costs by 25% or more.” 9 We abstract from migration and assume that the local population is fixed, as is the local supply of private religious schools, in relation to which the parameter zi is defined. Thus in a school district in which all religious schools were, say, Catholic, a Baptist parents might have a z value close to one while Jewish and Muslim parents had much lower z values. 10 There are conflicting opinions regarding the extent to which material resources—such as reduced class size—affect scholastic achievement and classroom behavior (Krueger, 1998; Card and Krueger, 1996; Hanushek, 1996; among others). However, for the purpose of our positive analysis it is parents’ perceptions that matter, i.e., it is sufficient that parents believe that their children will benefit from a larger school budget. 11 Public schooling in the United States is largely financed by a combination of property taxes and state grants, with local taxes determined by referenda on proposals set by a school board (Romer et al., 1992). We ignore these important institutional factors in the analysis, ignore external funding, and implicitly assume that incomes are perfectly correlated with property values. 12 Thus we abstract from the possibility of purchasing private education as a supplement to public schooling. We also ignore the fixed costs of education, which limit the variety of private schooling options in smaller communities. A uniform efficiency parameter for nonsectarian private schools could be incorporated in the model without difficulty, though its calibration raises some difficulties. 13 Hence we calibrate the distribution of ki, from which the distribution of zi can only be inferred by making an appropriate assumption on the size of h (see below). 14 From (3) and (5), yn ( t, q

e) = t Y / [qe (1 – t) (1 − α) αα/(1−α) ] ; it is possible of course that there are no households beyond this threshold, i.e., that f(y,k) = 0 for y > yn and k < 1.

15 From (3) and (7), yr (ki , t, q

e) = t Y / [ki qe (1 – t) (1 − α) αα/(1−α) ] , and again there may be no

households beyond this threshold for some or all values of k > 1. 16 We discuss popular support for the existence of public education in Section 5. 17 Ours are indicative rather than operational calibrations for predicting actual policy outcomes. Because of the local nature of school finance in the United States, outcomes are strongly affected by the concrete context of specific school districts. In addition we do not take into account important peer-group, housing and migration effects (see, e.g., Nechyba, 2000). Our analysis offers a methodology for incorporating the religious factor in more detailed analyses, as well as indicating its general strength and variability. 18 Per capita money income in that year was $20,120 and there were 2.61 persons per household (Statistical Abstract of the United States, 2000, Tables 737, 753, 63). 19 Spending per pupil is taken from the Digest of Educational Statistics (2000, Table 169). In 1997/8 there were 46,126,897 children in public schools and 5,076,119 in private schools, from which q is derived; m q -is the ratio of public school students to households, of which there were 101,041,000 in 1998 (Statistical Abstract of the United States, 2000, Table 63). 20 In 1997/8 the 4,279,146 pupils enrolled in private religious schools were 8.357% of total enrolment; and the 796,973 enrolled in nonsectarian private schools, 1.556% (Digest of Educational Statistics, 2000, Tables 41 and 60). 21 Data on private enrolment by state are tallied by the location of the school, not the hometown of the pupil. 22 As the vouchers we consider have little net fiscal effect, the assumption of a balanced budget has little effect on individual school choice (see also Section 5, below). 23 If vouchers are unrestricted, only households with ki < 1 choose private nonsectarian schooling. They maximize cα x 1− α subject to c + x m = (1 – t) yi + s m and x > s. As we have assumed that the subsidy is smaller than spending per pupil in public school and can only be used for private education, the second constraint is never binding: parents prefer nonsectarian private school to public school only if they intend to spend more than public spending per pupil. Hence such parents have yi > [α s m + (t Y – s m) / q] / [(1 − α) (1 – t)] > α s m / [(1 − α) (1 – t)]. 24 They maximize cα (ki x)1−α subject to c + x m = (1 – t) yi + s m and x > s, and must have ki > 1. A household with ki > x / s > 1 may choose to opt out of public education without adding to the sum of the voucher. 25 There may be no households with ki < 1 and income greater than the threshold yns. 26 Public spending per pupil increases holding the tax rate fixed if savings to the public system as a result of the reduced pupil load are greater than the cost of vouchers paid to pupils who would have attended private schools without the vouchers. This holds if public enrolment after the voucher is implemented is no greater than a threshold value q* given by t Y / q0 = [t Y – (1–q*) s m] / q* where q0 is public enrolment before the voucher program is implemented. Hoyt and Lee (1998, p. 224) calculate a related threshold and conclude that vouchers are likely to reduce taxes

holding public spending per pupil fixed. 27 This threshold value is yrn = s m / [( k 1–α –1) (1 – t) ] . 28See Appendix A for details of the derivation. 29 The large majority of households prefer means-tested vouchers to universal vouchers, as they generate a greater improvement in public school quality. 30 In the Cleveland voucher program, low-income families were required to contribute 10% of tuition, but participating schools accepted payment in kind, of parents’ time. 31 See Appendix B for details of the derivation. 32 In Milwaukee, where vouchers exceeding $5,000 are offered to families with incomes up to 175% of the poverty line, one third of recipients chose nonsectarian schools, almost exclusively in elementary schools. 33 Regressing the increase in religious enrolment on the mean and standard deviation of k yields the equation ∆qr = – 7.6 + 6.2 E(k) + 6.6 SD(k) with standard deviations 1.31 and 0.64, and an R2 of 0.86. The correlation coefficient between the increase in religious enrolment and prior religious enrolment in the state equals 0.71. 34 Again, we ignore important institutional aspects of the democratic process through which education budgets are determined as well as the nexus of state and local funding. 35 Letting θ (t0, s) denote the share of households receiving a voucher—the definition of θ (t0, s) will vary with the type of voucher program—spending per pupil in public schools is

),( 0 stx = [ t0 Y – θ (t0, s) s m ] / [q (t0, s) m ], which is maximized when – (∂q / ∂s ) ),( 0 stx = θ

(t0, s) + s (∂ θ / ∂ s ), where the derivatives of q and θ with respect to s are obtained by total differentiation of the relevant equilibrium conditions. 36 Alternatively, if voters are constrained to spend a given amount x0 per pupil in public schooling in voting on the amount of the voucher, the tax rate and voucher amount are linked by the equation ),( 0 stx = x0, which implicitly defines t as a function of s, and households anticipating sending their children to public schools seek to minimize the tax rate subject to this constraint, which similarly implies ∂ ),( stx / ∂ s = 0. 37 Increases in the tax rate are offset by increases in public enrolment, which dampen the effect of the tax rate on spending per pupil. The small size of the effect is also indirectly indicated by the small variations in spending, in Tables 5-7, when the voucher amount is changed: as the voucher has little effect on spending per student when the tax rate is held fixed, allowing the tax rate to vary should not result in much change in the chosen rate. Further details are available from the authors on request. 38 The emphasis on helping low-income families appears throughout the decision. Justice O’Connor emphasizes the small size of the program, noting that at most $8.2 million of public funds flowed to religious schools through it, which “pales in comparison to the amount of funds that federal, state and local governments already provide religious institutions.”

39 If k > 1 / q then k t Y > t Y / q which implies that household utility from an education voucher funded by all tax revenues is greater than utility from public schooling without vouchers, for a given tax rate. 40 This value is implicitly defined by [tY + (1 – t) ys] αα(1 − α)1−α = [(1 – t) ys]

α (tY / q)1−α which

equals $69,000 for our calibrated values, corresponding to the 77th percentile of the income distribution, i.e., 23% have incomes greater than ys , though just over half of these are included among the households with k > 1/q0. 41 This may deter all but the most committed and enterprising parents from opting out of the public system they know. Parents of weaker pupils are especially wary of privately managed schools, as was evident in the electoral defeat of an initiative to transfer five failing schools in New York City to private-sector management (New York Times, 2001b). 42 See, for example, Fernandez and Rogerson (1999) for a formal analysis of state and local funding of education in California. 43 This continues a long line of argument closely identified with Milton Friedman (1962, 2002), and appearing in Adam Smith (1776, Bk V, Ch 1, Art II) and Thomas Paine (1792). 44 Concern for damage to the fabric of society is raised in all the dissenting opinions to Zelman v. Simmons-Harris. Justice Stevens writes that, “Whenever we remove a brick from the wall that was designed to separate religion and government, we increase the risk of religious strife and weaken the foundation of our democracy.” Justice Breyer warns of “the risk that publicly financed voucher programs pose in terms of religiously based social conflict.” Conversely, Glazer (2001) has argued that in some cases parochial schools may be more faithful guardians of traditional American values than multi-cultural public schools.